I finished reading a book regarding the Cuban missle crisis. The book was written by the historian of the JFK library, and it was very interesting. However I still don't have a really good idea of how close the world came to a nuclear war.
If the U.S. had invaded Cuba, would the Cubans have been able to launch the Soviet nuclear missles?
There was an incident where a Russian sub thought it was under attack and almost launched a nuclear-tipped torpedo at a U.S. warship. The story goes that one out of the three Russian commanders on board the sub refused the launch, and so they didn't because they needed unanimous agreement. How sure are historians that this account is accurate? If a U.S. warship had been blown up by a nuclear torpedo, would the U.S. have responded with a nuclear strike on Cuba?
If the US had invaded Cuba, the local Soviet forces would very likely have used tactical nuclear weapons against the invading Americans. This would have been a catastrophe on the highest scale and could easily have led to further escalation.
The Cubans did not have access to the missiles themselves, but the Soviet forces on the island did.
The fear is not that this would proceed in a logical fashion ("oh, they did this, we should thus do this in response") but that you would get inadvertent escalation. To put it another way: even without nukes actually going off, both sides had numerous false alarms and "close calls" during the Crisis in which their soldiers thought that there was a possibility that nuclear weapons had already been ordered for use. In all of those cases it was discovered that this was false soon enough to avoid further escalation. If there actually were nukes going off, and the appearance of the beginning of a general war, would the number of mistakes and confusions multiply? If so, would restraint be used, or not? Keep in mind that at this point in history there were no significant "locks" or "codes" on most of the arsenals of either state — those in charge of them were restrained by regulations, not anything mechanical or physical.
It is telling that both the Soviet and US leadership, after the fact, believed they had avoided nuclear war by sheer luck, not by anything else.
As for Arkhipov — it's hard to sort out. There are mixed accounts. The most measured give Arkhipov a role in talking the others out of the use of a nuclear torpedo, but not necessarily being some kind of strong "veto." This is a subtle distinction. Either way, the story seems essentially accurate, even if perhaps too much attention is put on Arkhipov specifically.